I've dealt with this myself also, I'm assuming his inverter is either 12 or 24 volts DC input.
I'm betting that it's the same thing as what I was having with mine.
I was trying to use a small hand saw with mine, and it cuts out, only gets it going enough to rotate the blade for a second.
I have not tested this yet, so I don't know how effective it is.
I was going to get some of those car audio capacitors along the power rails, as close to the terminals of the inverter as possible, to handle the instantaneous spike in power consumption that occurs when the load starts.
I was having low voltage cut outs, so I figure, get 1 to 3 capacitors, to keep the constant current and handle increased demand.
~Kiyote!